Spectrally Perron Polynomials and the Cauchy-Ostrovsky Theorem

Pietro Paparella. "Spectrally Perron Polynomials and the Cauchy-Ostrovsky Theorem." Special Matrices 5.1 (2017): 123-126. <http://eudml.org/doc/288416>.

@article{PietroPaparella2017,
abstract = {In this note, we simplify the statements of theorems attributed to Cauchy and Ostrovsky and give proofs of each theorem via combinatorial and nonnegative matrix theory. We also show that each simple sufficient condition in each statement is also necessary in its respective case. In addition, we introduce the notion of a spectrally Perron polynomial and pose a problem that appeals to a wide mathematical audience.},
author = {Pietro Paparella},
journal = {Special Matrices},
keywords = {spectrally Perron polynomial; Cauchy Theorem; Ostrovsky Theorem; primitive matrix},
language = {eng},
number = {1},
pages = {123-126},
title = {Spectrally Perron Polynomials and the Cauchy-Ostrovsky Theorem},
url = {http://eudml.org/doc/288416},
volume = {5},
year = {2017},
}

TY - JOUR
AU - Pietro Paparella
TI - Spectrally Perron Polynomials and the Cauchy-Ostrovsky Theorem
JO - Special Matrices
PY - 2017
VL - 5
IS - 1
SP - 123
EP - 126
AB - In this note, we simplify the statements of theorems attributed to Cauchy and Ostrovsky and give proofs of each theorem via combinatorial and nonnegative matrix theory. We also show that each simple sufficient condition in each statement is also necessary in its respective case. In addition, we introduce the notion of a spectrally Perron polynomial and pose a problem that appeals to a wide mathematical audience.
LA - eng
KW - spectrally Perron polynomial; Cauchy Theorem; Ostrovsky Theorem; primitive matrix
UR - http://eudml.org/doc/288416
ER -